The wording in most of these "guarantees" to catch you up with the ship say something to the effect of "we will assist you" in getting to the next port and boarding the ship. First, that doesn't sound like a promise that they will get you there totally at their expense, no questions asked. Second, what, when and where is the next port? Many cruises start out with a day at sea, then may include a small out of the way port with limited air service. All depends on the itinerary. Third, who is paying for the hotel, food, other transport besides the flights, etc. Again, it doesn't sound like a guarantee to me. In a related subject, on our Copenhagen to Boston cruise this last summer, after sailing, we had a sea day, then a port day, then Alesund, Norway. The SAS airline strike was in progress. There was about 20 people (some were crew) waiting at the port when we docked (plus who knows how many others that arrived to catch up with the ship during that day), and a huge pile of baggage.
It always seems smarter to come in a day early to avoid possibly missing 2 or more days of your expensive cruise. The same thought applies to luggage.